{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.323139Z",
     "start_time": "2025-11-05T02:26:43.318059Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 108
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.345180Z",
     "start_time": "2025-11-05T02:26:43.338993Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 定义函数\n",
    "def J(x):\n",
    "    return (x ** 2 - 2) ** 2\n",
    "\n",
    "\n",
    "# 定义梯度函数（对于一元函数来说就是导函数）\n",
    "def gradient(x):\n",
    "    return 4 * x ** 3 - 8 * x"
   ],
   "id": "d9f0a9d5f6f6e111",
   "outputs": [],
   "execution_count": 109
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.380312Z",
     "start_time": "2025-11-05T02:26:43.374030Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 用列表保存点的变化轨迹\n",
    "x_list = []\n",
    "y_list = []"
   ],
   "id": "a7f210960390ab75",
   "outputs": [],
   "execution_count": 110
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.434265Z",
     "start_time": "2025-11-05T02:26:43.425518Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 定义超参数以及 x 的初始值\n",
    "alpha = 0.01\n",
    "x = 1"
   ],
   "id": "3e3ad37e4961cbc",
   "outputs": [],
   "execution_count": 111
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.512584Z",
     "start_time": "2025-11-05T02:26:43.493019Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#限制在一个极小值\n",
    "while np.abs(grad := gradient(x)) > 1e-10:\n",
    "    y = J(x)\n",
    "    # 记录当前点的坐标\n",
    "    x_list.append(x)\n",
    "    y_list.append(y)\n",
    "    print(f'x={x}, J({x})={y}')\n",
    "    # 计算梯度\n",
    "    # grad = gradient(x)\n",
    "    # 更新参数 x\n",
    "    x = x - alpha * grad\n",
    "print('x_list长度', ':', len(x_list))"
   ],
   "id": "ebd88506e59d9b59",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=1, J(1)=1\n",
      "x=1.04, J(1.04)=0.8434585599999997\n",
      "x=1.07820544, J(1.07820544)=0.7013610745610571\n",
      "x=1.1143241590355024, J(1.1143241590355024)=0.5749910889193622\n",
      "x=1.148123022342038, J(1.148123022342038)=0.4648696836477168\n",
      "x=1.179435254567999, J(1.179435254567999)=0.37079876554253405\n",
      "x=1.2081631119638494, J(1.2081631119638494)=0.29196936337312895\n",
      "x=1.2342759577740308, J(1.2342759577740308)=0.22711215958951933\n",
      "x=1.2578043609956837, J(1.2578043609956837)=0.17466397154551408\n",
      "x=1.2788312369671284, J(1.2788312369671284)=0.13292635472391318\n",
      "x=1.2974812343320477, J(1.2974812343320477)=0.10019912047177595\n",
      "x=1.313909549703096, J(1.313909549703096)=0.07487977735138664\n",
      "x=1.3282911671638526, J(1.3282911671638526)=0.05552742326314236\n",
      "x=1.3408112452155214, J(1.3408112452155214)=0.04089503341741407\n",
      "x=1.3516570783568256, J(1.3516570783568256)=0.029937007850226644\n",
      "x=1.36101179656952, J(1.36101179656952)=0.021799604008143292\n",
      "x=1.3690497629083402, J(1.3690497629083402)=0.015801180523051447\n",
      "x=1.3759334955299414, J(1.3759334955299414)=0.011407738640925019\n",
      "x=1.3818118695581485, J(1.3818118695581485)=0.008207627451601108\n",
      "x=1.3868193323150038, J(1.3868193323150038)=0.0058878212349127105\n",
      "x=1.391075876894707, J(1.391075876894707)=0.0042130360953512025\n",
      "x=1.394687549713828, J(1.394687549713828)=0.0030081537737527775\n",
      "x=1.3977473066778767, J(1.3977473066778767)=0.002143918420165555\n",
      "x=1.4003360726013632, J(1.4003360726013632)=0.0015255964014669267\n",
      "x=1.402523895157388, J(1.402523895157388)=0.001084169121271803\n",
      "x=1.4043711158180114, J(1.4043711158180114)=0.0007696057503605176\n",
      "x=1.4059295053845733, J(1.4059295053845733)=0.0005457935984928247\n",
      "x=1.4072433310921304, J(1.4072433310921304)=0.0003867597015712618\n",
      "x=1.4083503366435202, J(1.4083503366435202)=0.0002738802994882323\n",
      "x=1.409282626781808, J(1.409282626781808)=0.00019383538951067927\n",
      "x=1.410067455028093, J(1.410067455028093)=0.00013711876662924233\n",
      "x=1.4107279177794754, J(1.4107279177794754)=9.695832796702077e-05\n",
      "x=1.411283560732882, J(1.411283560732882)=6.853705921774495e-05\n",
      "x=1.4117509050939956, J(1.4117509050939956)=4.8432997352643364e-05\n",
      "x=1.4121439016455875, J(1.4121439016455875)=3.421783238774052e-05\n",
      "x=1.4124743207833077, J(1.4124743207833077)=2.416993811780025e-05\n",
      "x=1.4127520862951624, J(1.4127520862951624)=1.7069644823008688e-05\n",
      "x=1.4129855601161534, J(1.4129855601161534)=1.2053443173386492e-05\n",
      "x=1.413181784637025, J(1.413181784637025)=8.51031004736709e-06\n",
      "x=1.4133466884560102, J(1.4133466884560102)=6.008078624674287e-06\n",
      "x=1.4134852607800472, J(1.4134852607800472)=4.241200676394194e-06\n",
      "x=1.4136016990345834, J(1.4136016990345834)=2.993718299350918e-06\n",
      "x=1.4136995336440676, J(1.4136995336440676)=2.1130360327356864e-06\n",
      "x=1.4137817334055847, J(1.4137817334055847)=1.4913545692276398e-06\n",
      "x=1.4138507943975371, J(1.4138507943975371)=1.0525347890777745e-06\n",
      "x=1.413908814942173, J(1.413908814942173)=7.428078804467233e-07\n",
      "x=1.4139575587715218, J(1.4139575587715218)=5.242078461715436e-07\n",
      "x=1.4139985082263038, J(1.4139985082263038)=3.69930028130032e-07\n",
      "x=1.4140329090415937, J(1.4140329090415937)=2.610516592140457e-07\n",
      "x=1.4140618080364205, J(1.4140618080364205)=1.842152605066583e-07\n",
      "x=1.414086084822213, J(1.414086084822213)=1.2999248948460152e-07\n",
      "x=1.4141064784726312, J(1.4141064784726312)=9.172874783601499e-08\n",
      "x=1.4141236099507466, J(1.4141236099507466)=6.47273890462156e-08\n",
      "x=1.414138000965189, J(1.414138000965189)=4.56737704714294e-08\n",
      "x=1.4141500898215325, J(1.4141500898215325)=3.222867188314084e-08\n",
      "x=1.4141602447460886, J(1.4141602447460886)=2.2741297397075685e-08\n",
      "x=1.4141687750839818, J(1.4141687750839818)=1.6046701927536052e-08\n",
      "x=1.4141759407098307, J(1.4141759407098307)=1.1322815152671593e-08\n",
      "x=1.4141819599357555, J(1.4141819599357555)=7.989533826927347e-09\n",
      "x=1.4141870161562438, J(1.4141870161562438)=5.637507209735755e-09\n",
      "x=1.414191263431349, J(1.414191263431349)=3.977879701092322e-09\n",
      "x=1.4141948311776438, J(1.4141948311776438)=2.8068242876353354e-09\n",
      "x=1.4141978281093737, J(1.4141978281093737)=1.980514403824722e-09\n",
      "x=1.4142003455495558, J(1.4142003455495558)=1.3974623353855156e-09\n",
      "x=1.4142024602116772, J(1.4142024602116772)=9.86056164198191e-10\n",
      "x=1.4142042365365866, J(1.4142042365365866)=6.957652245185569e-10\n",
      "x=1.4142057286556684, J(1.4142057286556684)=4.9093431033722e-10\n",
      "x=1.4142069820400422, J(1.4142069820400422)=3.464046528600686e-10\n",
      "x=1.4142080348859822, J(1.4142080348859822)=2.4442395491570984e-10\n",
      "x=1.4142089192787353, J(1.4142089192787353)=1.724660356370887e-10\n",
      "x=1.4142096621701743, J(1.4142096621701743)=1.2169232697162548e-10\n",
      "x=1.41421028620006, J(1.41421028620006)=8.586627912121184e-11\n",
      "x=1.414210810385924, J(1.414210810385924)=6.058734921217195e-11\n",
      "x=1.4142112507025861, J(1.4142112507025861)=4.275049445481244e-11\n",
      "x=1.4142116205689608, J(1.4142116205689608)=3.016478494901903e-11\n",
      "x=1.4142119312569823, J(1.4142119312569823)=2.128429363746113e-11\n",
      "x=1.4142121922351087, J(1.4142121922351087)=1.5018210261923213e-11\n",
      "x=1.414212411456868, J(1.414212411456868)=1.059685667077154e-11\n",
      "x=1.4142125956032394, J(1.4142125956032394)=7.477146519032887e-12\n",
      "x=1.4142127502862578, J(1.4142127502862578)=5.27587722030844e-12\n",
      "x=1.4142128802200398, J(1.4142128802200398)=3.722660531297792e-12\n",
      "x=1.4142129893644497, J(1.4142129893644497)=2.6267101966146385e-12\n",
      "x=1.4142130810457771, J(1.4142130810457771)=1.8534072649497906e-12\n",
      "x=1.4142131580581088, J(1.4142131580581088)=1.307764491172204e-12\n",
      "x=1.4142132227484787, J(1.4142132227484787)=9.227588185933946e-13\n",
      "x=1.4142132770883977, J(1.4142132770883977)=6.510987369675258e-13\n",
      "x=1.4142133227339355, J(1.4142133227339355)=4.594153363978507e-13\n",
      "x=1.4142133610761913, J(1.4142133610761913)=3.241635014026636e-13\n",
      "x=1.4142133932836891, J(1.4142133932836891)=2.2872979033478537e-13\n",
      "x=1.4142134203379892, J(1.4142134203379892)=1.613917539473932e-13\n",
      "x=1.4142134430636026, J(1.4142134430636026)=1.1387803018733294e-13\n",
      "x=1.414213462153119, J(1.414213462153119)=8.035234298446954e-14\n",
      "x=1.4142134781883136, J(1.4142134781883136)=5.6696616124099714e-14\n",
      "x=1.4142134916578775, J(1.4142134916578775)=4.000513397151791e-14\n",
      "x=1.4142135029723115, J(1.4142135029723115)=2.822762344952011e-14\n",
      "x=1.4142135124764363, J(1.4142135124764363)=1.991741170012989e-14\n",
      "x=1.4142135204599013, J(1.4142135204599013)=1.4053726034652345e-14\n",
      "x=1.4142135271660121, J(1.4142135271660121)=9.916309249252413e-15\n",
      "x=1.4142135327991452, J(1.4142135327991452)=6.996947947431361e-15\n",
      "x=1.414213537530977, J(1.414213537530977)=4.937046539107209e-15\n",
      "x=1.4142135415057158, J(1.4142135415057158)=3.483580096706623e-15\n",
      "x=1.4142135448444964, J(1.4142135448444964)=2.4580141408954754e-15\n",
      "x=1.414213547649072, J(1.414213547649072)=1.734374814804771e-15\n",
      "x=1.4142135500049158, J(1.4142135500049158)=1.2237748562765541e-15\n",
      "x=1.4142135519838244, J(1.4142135519838244)=8.634955542483674e-16\n",
      "x=1.4142135536461076, J(1.4142135536461076)=6.092824793010257e-16\n",
      "x=1.4142135550424255, J(1.4142135550424255)=4.299097254977233e-16\n",
      "x=1.4142135562153326, J(1.4142135562153326)=3.0334430354873035e-16\n",
      "x=1.4142135572005745, J(1.4142135572005745)=2.1403974864034885e-16\n",
      "x=1.4142135580281778, J(1.4142135580281778)=1.5102644205629874e-16\n",
      "x=1.4142135587233646, J(1.4142135587233646)=1.065642558645651e-16\n",
      "x=1.4142135593073215, J(1.4142135593073215)=7.519173847593654e-17\n",
      "x=1.4142135597978454, J(1.4142135597978454)=5.3055288727798327e-17\n",
      "x=1.4142135602098853, J(1.4142135602098853)=3.743581042210181e-17\n",
      "x=1.414213560555999, J(1.414213560555999)=2.6414708381612764e-17\n",
      "x=1.4142135608467343, J(1.4142135608467343)=1.8638217160421628e-17\n",
      "x=1.414213561090952, J(1.414213561090952)=1.3151125319788258e-17\n",
      "x=1.4142135612960949, J(1.4142135612960949)=9.279434296200959e-18\n",
      "x=1.4142135614684148, J(1.4142135614684148)=6.547570248467442e-18\n",
      "x=1.4142135616131637, J(1.4142135616131637)=4.619965185506628e-18\n",
      "x=1.4142135617347527, J(1.4142135617347527)=3.259847787687766e-18\n",
      "x=1.4142135618368874, J(1.4142135618368874)=2.3001488414583943e-18\n",
      "x=1.4142135619226806, J(1.4142135619226806)=1.6229855203964223e-18\n",
      "x=1.414213561994747, J(1.414213561994747)=1.1451786592290388e-18\n",
      "x=1.4142135620552827, J(1.4142135620552827)=8.080376946917743e-19\n",
      "x=1.4142135621061327, J(1.4142135621061327)=5.70151169353862e-19\n",
      "x=1.4142135621488467, J(1.4142135621488467)=4.022983946904878e-19\n",
      "x=1.4142135621847265, J(1.4142135621847265)=2.8386167158005875e-19\n",
      "x=1.4142135622148655, J(1.4142135622148655)=2.002926523683161e-19\n",
      "x=1.4142135622401821, J(1.4142135622401821)=1.4132666913737516e-19\n",
      "x=1.4142135622614482, J(1.4142135622614482)=9.972013700960141e-20\n",
      "x=1.4142135622793117, J(1.4142135622793117)=7.036253338592764e-20\n",
      "x=1.414213562294317, J(1.414213562294317)=4.964775606063605e-20\n",
      "x=1.4142135623069216, J(1.4142135623069216)=3.503138353186975e-20\n",
      "x=1.4142135623175094, J(1.4142135623175094)=2.4718133048932092e-20\n",
      "x=1.4142135623264032, J(1.4142135623264032)=1.7441053684879287e-20\n",
      "x=1.4142135623338739, J(1.4142135623338739)=1.2306435068299821e-20\n",
      "x=1.4142135623401493, J(1.4142135623401493)=8.683405686535936e-21\n",
      "x=1.4142135623454206, J(1.4142135623454206)=6.1270013192922704e-21\n",
      "x=1.4142135623498486, J(1.4142135623498486)=4.323159572184818e-21\n",
      "x=1.414213562353568, J(1.414213562353568)=3.050406677757899e-21\n",
      "x=1.4142135623566925, J(1.4142135623566925)=2.1523620071325393e-21\n",
      "x=1.4142135623593168, J(1.4142135623593168)=1.5187080167464017e-21\n",
      "x=1.4142135623615213, J(1.4142135623615213)=1.0716189845651673e-21\n",
      "x=1.4142135623633731, J(1.4142135623633731)=7.561280055323836e-22\n",
      "x=1.4142135623649286, J(1.4142135623649286)=5.335263825384799e-22\n",
      "x=1.4142135623662353, J(1.4142135623662353)=3.7644759913661035e-22\n",
      "x_list长度 : 147\n"
     ]
    }
   ],
   "execution_count": 112
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:43.790498Z",
     "start_time": "2025-11-05T02:26:43.611106Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 画图\n",
    "x = np.arange(0.9, 1.6, 0.01)\n",
    "plt.plot(x, J(x))\n",
    "plt.plot(x_list, y_list, 'r')\n",
    "plt.scatter(x_list, y_list, color='red')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('J(x)')\n",
    "plt.show()"
   ],
   "id": "dd9203b81222c514",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 113
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-05T02:26:44.166824Z",
     "start_time": "2025-11-05T02:26:43.824902Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 进行数据局部放大\n",
    "fig, ax = plt.subplots(1, 2, figsize=(15, 4))\n",
    "ax[0].plot(x, J(x))\n",
    "ax[0].plot(x_list, y_list, 'r')\n",
    "ax[0].scatter(x_list, y_list, color='red')\n",
    "\n",
    "x_list2 = x_list[1:]\n",
    "y_list2 = y_list[1:]\n",
    "x = np.arange(1.399, 1.425, 0.001)\n",
    "ax[1].plot(x, J(x))\n",
    "ax[1].plot(x_list2, y_list2, 'r')\n",
    "ax[1].scatter(x_list2, y_list2, color='red')"
   ],
   "id": "a0b4b34ce5a8b3b1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x13ca70e1bd0>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x400 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 114
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
